Is possible to switch in a new Tamron SP AF 70-200mm f/2.8 DI LD(IF)Macro for Sony, the mount bayonet of the same model lens, but made for Nikon?
In practice: Too much may be involved. Mostly as per @jwenting's advice.
There is a better reason not to do it than that it may not work.
A look through related ebay listings suggests that, in equivalent condition, the price of the Sony version is equal to or somewhat greater than Nikon versions. A sell-buy would avoid the significant complexities.
But, better still, unless $ are severely limited, the newer stabilised Tamron SP 70-200mm f/2.8 Di VC USD for Nikon (MPN:AFA009N-700) is more expensive but both usefully superior optically and has internal stabilisation in the Nikon version. (The Sony version has not been equipped with stabilisation, alas).
Also worth considering is the newer Sigma stabilised 70-200mm f/2.8 for Nikom. This is user switchable to have either 'usual' stabiisation or pan only stabilisation or none. Unlike the Tamron version, this has stabilisation included in the Sony version. This lens is not quite as good optically as the stabilised Tamron but arguably superior to your existing Tamron, and is usually lower cost than the stabilised Tamron.
Not relevant to your query but of general applicability and may help some: I bought a Sony A-mount Sigma 70-200mm f2.8 in preference to the Tamron due to Sigma retaining stabilisation in the Sony version. This allows me to use it with stabilisation with APSC E-mount Sony bodies and using panning stabilisation with A-mount bodies. While the slightly superior optical results of the Tamron would have been preferred the useful gains from stabilisation in eg e-mount use made the Sigma more attractive (to me).
Highly unlikely. It's technically possible to convert a lens to work with another brand body, but it involves a lot more than "just" changing out the bayonet flange.
The internal electronics of the lens need to be replaced, the travel range of the various control rings will differ between brands, sometimes being actually reversed from another one.
And worst of all, the diameter of the lens (and thus the lens opening, aperture rings, bayonet ring, etc. etc. are different between camera brands as well.
Unless your lens is extremely expensive and rare it's almost certainly cheaper to just replace it. And if it is it's too risky to risk losing it if the conversion doesn't work so you're better off keeping a camera body that'll work with it.